A Leland Model for Delta Hedging in Central Risk Books

Abstract

Using a tractable extension of the Leland (1985) model, we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid-ask spreads, and volatilities. The corresponding option price (from which the option can be replicated using market and limit orders) is characterized via a nonlinear PDE.

Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced-form models are competitive with "brute force" numerical approaches to market microstructure. Both the estimation of microstructure parameters, and the simulation of the optimal trading strategy are made concrete and reconciled with real-life high frequency data.

Keywords: Market microstructure, market making, central risk book, limit orders, adverse selection

JEL Classification: C61, G13, G14